Materials

  • CCB Mathematics pages 190 - 199

Standards

  • Investigate chance processes and develop, use, and evaluate probability models.

Objectives

  • Describe the information that a trend line provides about two correlated variables

  • Describe various aspects of the correlation between two variables

Key Concept

  • We can use the concept of correlation to describe the relationship between two variables that generally follow a linear pattern but cannot be described by a linear equation. Plotting data on a scatter plot and constructing a trend line can determine the strength and direction of the correlation between such variables.

Vocabulary

Tier 2 Cluster
Correlation
Tier 3 Outlier
Trend Lines
Test Words Scatter Plots

Before Lesson

In this lesson, students learn to plot data on a scatter plot and construct trend lines to determine the direction and strength of the correlation between the variables. To determine student readiness for the lesson, write a set of points on the board and have students plot them on a coordinate plane. Observe students as they work to offer guidance, if necessary.

Background

Tell students that correlation is described in terms of direction and strength. Linearly correlated data that has a trend line with a positive slope is positively correlated, whereas if the trend line has a negative slope, the data are negatively correlated. Data that are strongly correlated are located, on average, close to a trend line. Data that are weakly correlated are located farther away from a trend line.

Guided Practice

  • Scatter Plots
  • Linear Correlations
  • Nonlinear Correlations
  • Outliers and Clusters

Core Skill

Represent Real-World Problems: Read this exercise together, emphasizing that data have no value unless they are analyzed to look for relationships among variables. Examine the scatter plot as a class, and ask a volunteer to describe the relationship among the data in terms of correlation strength and direction.

Interpret Data Displays: Give students time to draw trend lines in the scatter plots and use the lines they draw to explain the relationship between each pair of variables.

Extension

Retell: Invite volunteers to identify the scatter plot in the lesson that they found most interesting. Have them explain the scatter plot’s variables and the trend line’s strength and direction. Invite them to explain why they found this scatter plot so interesting. Assist students if they are having trouble understanding what a trend line represents.

Two Sources of Information: Have students use print or online materials to find two real-world examples of scatter plots. Ask students to describe the scatter plots’ common characteristics and what conclusions can be drawn from trend lines.